Patricia Bean

2022-07-17

A spring balance has a scale that reads from 0 to 50 kg.The length of the scale is 20 cm.A block of mass m is suspended from this balance,when displaced and released,it oscillates with a period 0.5 s. What is the value of m?[$g=10m{s}^{-2}$]

Monica Dennis

Expert

I am guessing that the wording of the question means that the spring stretches from 0 to 20 cm as the weight increases from 0N to 500 N. This means that the spring constant is
$k=\frac{500N}{0.2m}=2500N{m}^{-1}$
The time period of oscillations of a mass m attached to a spring with spring constant k is given by
$T=2\pi \sqrt{\frac{m}{k}}$
Thus
$m=k\left(\frac{T}{2\pi }{\right)}^{2}\approx 2500N{m}^{-1}\left(\frac{0.5s}{2×3.14}{\right)}^{2}=15.8Kg$

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